Boris Kruglikov
“Poincare functions for some geometric structures”
Poincare function is a rational function encoding the number of differential invariants of a pseudo-group action depending on the jet-order. I review the situation with the action of the diffeomorphisms group acting on natural bundles, and describe the Poincare function for a variety of important geometric structures: metrics (with various specifications), connections (with specifications), conformal structures etc. This surveys the works by many mathematicians starting from Tresse, Thomas, to more recent: Shmelev, Dubrovskiy, Lychagin and Yumaguzhin, together with my recent work.